The question of adaptive sampling comes back often even though the initial intent of compressed sensing is to have a linear acquisition process. In effect, if one is to nonlinearly acquire signals, how is that different from JPEG and more specialized compression techniques ? Well for one, if we had to wait for a standard like JPEG for high-dimensional signals, we'd have to wait for a long, no make that a looooooong time. Hence it becomes obvious that one should look at CS as a way to perform a nonlinear compr
ession scheme in fields where
the amount of (economic?) interest is very restricted. Here is the latest entry on this matter:
Sequential adaptive compressed sampling via Huffman codes by Akram Aldroubi, Haichao Wang, Kourosh Zarringhalam. The abstract reads:
There are two main approaches in compressed sensing: the geometric approach and the combinatorial approach. In this paper we introduce an information theoretic approach and use results from the theory of Huffman codes to construct a sequence of binary sampling vectors to determine a sparse
signal. Unlike other approaches, our approach is adaptive in the sense that each sampling vector depends on the previous sample. The number of measurements we
need for a k-sparse vector in n-dimensional space is no more than O(k log n) and the reconstruction is O(k).
The O(k log n) result is very interesting but I am a little bothered about the "unlike other approaches.." as "unlike most other approaches.." would have
sufficed. We have seen adaptive measurements before (as listed in the Big Picture page ):
3.2 Non-Deterministic and Adaptive Measurement codes/matrices as mentioned here (as well as new ones).
I have mentioned them before, but let me do this again as
their webpage has been substantially updated: The Compressive Structured Light for Recovering Inhomogeneous Participating Media is here:
Let us note the following in the page:
In our experiment, we use the vertical binary stripe patterns as the coded light pattern. Each frame has 128 stripes. The stripes are randomly assigned to be 0 (black) or 1 (white) according to Bernoulli distribution (with p=0.5). We also tried Hadamard codes and found that the Bernoulli random code is better.
I am sure they will also be able to use adaptive measurements at some point in time.
Image Credit: NASA/JPL/Space Science Institute, Have you ever seen star shining through Saturn's ring ? W00050600.jpg was taken on October 28, 2008 and received on Earth October 29, 2008.